Effective theory for stochastic particle acceleration, with application to magnetized turbulence

TL;DR

This paper develops an effective theoretical framework for stochastic particle acceleration in turbulent plasmas, integrating statistical models with turbulence analysis, and applies it to magnetohydrodynamic turbulence to understand acceleration mechanisms.

Contribution

It introduces a comprehensive effective theory for stochastic Fermi acceleration applicable to generic settings and connects particle energization to turbulence statistics.

Findings

Acceleration peaks at scales with particle trapping or sharp magnetic bends

The formalism matches well with existing numerical results

Inhomogeneous, rapid acceleration regimes are identified

Abstract

The physics of particle acceleration in turbulent plasmas is a topic of broad interest, which is making rapid progress thanks to dedicated, large-scale numerical experiments. The first part of this paper presents an effective theory of stochastic Fermi acceleration, which subsumes all forms of non-resonant acceleration in ideal electric fields and is applicable in generic settings. It combines an exact equation connecting the energization rate to the statistics of the velocity field with a statistical model of particle transport through the structures (i.e., the regions of strong velocity gradients). In a second part, this formalism is applied to magnetohydrodynamic turbulence to obtain a comprehensive assessment of the scale-by-scale contributions to the advection and diffusion coefficients. Acceleration peaks on scales where particles can be trapped inside structures for an eddy turn-around time, or in intense structures associated with sharp bends of the magnetic field lines in large-amplitude turbulence (as reported earlier). These spatially inhomogeneous, rapid acceleration regimes pave the way for a rich phenomenology. We discuss the scalings obtained, their interpretation and show that the findings compare satisfactorily with existing numerical results.